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Statistica Sinica 15(2005), 3-18



Yves F. Atchadé and François Perron

Harvard University and University of Montreal

Abstract: This paper proposes methods to improve Monte Carlo estimates when the Independent Metropolis-Hastings Algorithm (IMHA) is used. Our first approach uses a control variate based on the sample generated by the proposal distribution. We derive the variance of our estimator for a fixed sample size $n$ and show that, as $n$ tends to infinity, this variance is asymptotically smaller than the one obtained with the IMHA. Our second approach is based on Jensen's inequality. We use a Rao-Blackwellization and exploit the lack of symmetry in the IMHA. An upper bound on the improvements that we can obtain by these methods is derived.

Key words and phrases: Control variates, Metropolis-hastings algorithm, Rao-Blackwellization, symmetry.

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